Pauli group: Classification and joint higher rank numerical range

In Mousavi and Salemi (2015) [17], authors showed that joint higher rank numerical range of triple of Pauli group elements is often convex, and characterized it exactly in the case that it is convex. In the present paper, those results are derived in a different manner. Also, N-qubit Pauli group using simultaneously unitary similarity are classified, which may generally be used to characterize joint higher rank numerical range of any Hermitian m-tuple in the N-qubit Pauli group. Besides, some more results about joint numerical range are here derived.